Chaotic finite difference operators

Marina Murillo-Arcila; Alfred Peris; Álvaro Vargas

doi:10.1063/5.0158038

Chaotic finite difference operators

Chaos. 2023 Sep 1;33(9):093111. doi: 10.1063/5.0158038.

Authors

Marina Murillo-Arcila¹, Alfred Peris², Álvaro Vargas²

Affiliations

¹ Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Spain.
² Institut Universitari de Matemática Pura i Aplicada, Universitat Politècnica de València, 46022 València, Spain.

PMID: 37695927
DOI: 10.1063/5.0158038

Abstract

In this article, we analyze the chaotic behavior of finite difference operators associated with certain differential equations. Our examples range from numerical schemes for a birth-and-death model with proliferation to a class of second-order partial differential equations that includes the hyperbolic heat transfer equation, the telegraph equation, and the wave equation. We provide sufficient conditions on the spatial and time steps of the scheme that guarantee chaos for the corresponding operators, and we compare them with the conditions needed to ensure chaotic analytical solutions.